In general, computing the exact minimum distance for
general linear codes is NP-hard [1]} and very difficult for linear codes with large lengths and dimensions.
In [2]}, the authors used the fixed subcode by the action of multipliers to find an upper bound (or even the exact value) for the minimum distance of certain linear cyclic codes.
In this section, we extend the theory of fixed subcodes by the action of multipliers and determine a new minimum distance lower bound for linear cyclic codes over \(\mathbb {F}_4\) .
